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arXiv2026

A Survey of Graph Transformers: Architectures, Theories and Applications

Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed diverse architectures, enhanced explainability, and practical applications for Graph Transformers. In light of these rapid developments, we conduct a comprehensive review of Graph Transformers, covering aspects such as their architectures, theoretical foundations, and applications. In this survey, we first categorize the architecture of Graph Transformers according to their strategies for processing structural information, including graph tokenization, positional encoding, structure-aware attention, and model ensemble. Then, from the theoretical perspective, we examine the expressivity of Graph Transformers in various discussed architectures and contrast them with other advanced graph learning algorithms to discover their connections. For applications, we organize the literature around four graph organization forms, from relational, geometric, dynamic to heterogeneous. A Practical Guidance table then maps architectural components to these graph forms by adoption frequency, so practitioners can narrow down which design families to consider for a given input structure. Lastly, we will discuss the current challenges and prospective directions in Graph Transformers for potential future research.

cs.LG↗

arXiv2026

Variational Quantum Transformer Architecture for Synthetic Language Generation

We propose a compact NISQ-compatible quantum transformer architecture for synthetic QNLP sequence modelling. The model preserves the autoregressive next-token interface of a classical transformer, but replaces attention and feed-forward sublayers with variational quantum encoder blocks, connector circuits, decoder blocks and a direct two-qubit measurement readout. Token contexts are angle-encoded into small quantum registers, processed by parallel variational heads and encoder integration circuits and conditioned through decoder ancillae to produce a distribution over a four-token vocabulary. We evaluate several architecture variants on deterministic and lexicographic grammar-generation tasks against a compact classical transformer baseline. The quantum models are trainable end-to-end and learn nontrivial grammar structure, including perfect deterministic generation in individual runs and high lexicographic validity in the strongest variant. The classical baseline remains more accurate and stable and the quantum models are sensitive to initialization. The contribution is therefore not a claim of quantum advantage, but a concrete architecture and evaluation of transformer-inspired QNLP sequence modelling under near-term quantum constraints.

quant-ph↗

arXiv2023

Building Blocks for a Complex-Valued Transformer Architecture

Most deep learning pipelines are built on real-valued operations to deal with real-valued inputs such as images, speech or music signals. However, a lot of applications naturally make use of complex-valued signals or images, such as MRI or remote sensing. Additionally the Fourier transform of signals is complex-valued and has numerous applications. We aim to make deep learning directly applicable to these complex-valued signals without using projections into $\mathbb{R}^2$. Thus we add to the recent developments of complex-valued neural networks by presenting building blocks to transfer the transformer architecture to the complex domain. We present multiple versions of a complex-valued Scaled Dot-Product Attention mechanism as well as a complex-valued layer normalization. We test on a classification and a sequence generation task on the MusicNet dataset and show improved robustness to overfitting while maintaining on-par performance when compared to the real-valued transformer architecture.

cs.LG↗

arXiv2024

EchoPT: A Pretrained Transformer Architecture that Predicts 2D In-Air Sonar Images for Mobile Robotics

The predictive brain hypothesis suggests that perception can be interpreted as the process of minimizing the error between predicted perception tokens generated by an internal world model and actual sensory input tokens. When implementing working examples of this hypothesis in the context of in-air sonar, significant difficulties arise due to the sparse nature of the reflection model that governs ultrasonic sensing. Despite these challenges, creating consistent world models using sonar data is crucial for implementing predictive processing of ultrasound data in robotics. In an effort to enable robust robot behavior using ultrasound as the sole exteroceptive sensor modality, this paper introduces EchoPT, a pretrained transformer architecture designed to predict 2D sonar images from previous sensory data and robot ego-motion information. We detail the transformer architecture that drives EchoPT and compare the performance of our model to several state-of-the-art techniques. In addition to presenting and evaluating our EchoPT model, we demonstrate the effectiveness of this predictive perception approach in two robotic tasks.

cs.RO↗

arXiv2024

Extra Global Attention Designation Using Keyword Detection in Sparse Transformer Architectures

In this paper, we propose an extension to Longformer Encoder-Decoder, a popular sparse transformer architecture. One common challenge with sparse transformers is that they can struggle with encoding of long range context, such as connections between topics discussed at a beginning and end of a document. A method to selectively increase global attention is proposed and demonstrated for abstractive summarization tasks on several benchmark data sets. By prefixing the transcript with additional keywords and encoding global attention on these keywords, improvement in zero-shot, few-shot, and fine-tuned cases is demonstrated for some benchmark data sets.

cs.CL↗

arXiv2026

Lightweight Transformer Architectures for Edge Devices in Real-Time Applications

The deployment of transformer-based models on resource-constrained edge devices represents a critical challenge in enabling real-time artificial intelligence applications. This comprehensive survey examines lightweight transformer architectures specifically designed for edge deployment, analyzing recent advances in model compression, quantization, pruning, and knowledge distillation techniques. We systematically review prominent lightweight variants including MobileBERT, TinyBERT, DistilBERT, EfficientFormer, EdgeFormer, and MobileViT, providing detailed performance benchmarks on standard datasets such as GLUE, SQuAD, ImageNet-1K, and COCO. Our analysis encompasses current industry adoption patterns across major hardware platforms (NVIDIA Jetson, Qualcomm Snapdragon, Apple Neural Engine, ARM architectures), deployment frameworks (TensorFlow Lite, ONNX Runtime, PyTorch Mobile, CoreML), and optimization strategies. Experimental results demonstrate that modern lightweight transformers can achieve 75-96% of full-model accuracy while reducing model size by 4-10x and inference latency by 3-9x, enabling deployment on devices with as little as 2-5W power consumption. We identify sparse attention mechanisms, mixed-precision quantization (INT8/FP16), and hardware-aware neural architecture search as the most effective optimization strategies. Novel findings include memory-bandwidth bottleneck analysis revealing 15-40M parameter models achieve optimal hardware utilization (60-75% efficiency), quantization sweet spots for different model types, and comprehensive energy efficiency profiling across edge platforms. We establish real-time performance boundaries and provide a practical 6-step deployment pipeline achieving 8-12x size reduction with less than 2% accuracy degradation.

cs.LG↗

arXiv2025

Application of Tabular Transformer Architectures for Operating System Fingerprinting

Operating System (OS) fingerprinting is essential for network management and cybersecurity, enabling accurate device identification based on network traffic analysis. Traditional rule-based tools such as Nmap and p0f face challenges in dynamic environments due to frequent OS updates and obfuscation techniques. While Machine Learning (ML) approaches have been explored, Deep Learning (DL) models, particularly Transformer architectures, remain unexploited in this domain. This study investigates the application of Tabular Transformer architectures-specifically TabTransformer and FT-Transformer-for OS fingerprinting, leveraging structured network data from three publicly available datasets. Our experiments demonstrate that FT-Transformer generally outperforms traditional ML models, previous approaches and TabTransformer across multiple classification levels (OS family, major, and minor versions). The results establish a strong foundation for DL-based OS fingerprinting, improving accuracy and adaptability in complex network environments. Furthermore, we ensure the reproducibility of our research by providing an open-source implementation.

cs.CR↗

arXiv2025

Machine learning revolution for exoplanet direct imaging detection: transformer architectures

Directly imaging exoplanets is a formidable challenge due to extreme contrast ratios and quasi-static speckle noise, motivating the exploration of advanced post-processing methods. While Convolutional Neural Networks (CNNs) have shown promise, their inherent limitations in capturing long-range dependencies in image sequences hinder their effectiveness. This study introduces a novel hybrid deep learning architecture that combines a CNN feature extractor with a Transformer encoder to leverage temporal information, modeling the signature of a planet's coherent motion across an observation sequence. We first validated the model on a purely synthetic dataset, where it demonstrated excellent performance. While the final metrics varied slightly between training runs, our reported trial achieved 100.0% accuracy, a 100.0% F1-score, and a position accuracy of 0.72 pixels, showing strong results on this specific test case in comparison to traditional methods like median subtraction and PCA-KLIP. To assess its viability on realistic data, we retrained the model on a semi-synthetic dataset created by injecting planet signals into actual high-contrast imaging observations of the TW Hya protoplanetary disk from JWST. The model successfully identified the injected signals with high confidence, confirming its ability to function amidst complex, correlated noise and bright disk features. This work serves as a successful proof-of-concept, demonstrating that a CNN-Transformer architecture holds significant promise as a fast, accurate, and automated method for exoplanet detection in the large datasets expected from current and future high-contrast imaging instruments.

astro-ph.EP↗

arXiv2022

Defect Transformer: An Efficient Hybrid Transformer Architecture for Surface Defect Detection

Surface defect detection is an extremely crucial step to ensure the quality of industrial products. Nowadays, convolutional neural networks (CNNs) based on encoder-decoder architecture have achieved tremendous success in various defect detection tasks. However, due to the intrinsic locality of convolution, they commonly exhibit a limitation in explicitly modeling long-range interactions, critical for pixel-wise defect detection in complex cases, e.g., cluttered background and illegible pseudo-defects. Recent transformers are especially skilled at learning global image dependencies but with limited local structural information necessary for detailed defect location. To overcome the above limitations, we propose an efficient hybrid transformer architecture, termed Defect Transformer (DefT), for surface defect detection, which incorporates CNN and transformer into a unified model to capture local and non-local relationships collaboratively. Specifically, in the encoder module, a convolutional stem block is firstly adopted to retain more detailed spatial information. Then, the patch aggregation blocks are used to generate multi-scale representation with four hierarchies, each of them is followed by a series of DefT blocks, which respectively include a locally position-aware block for local position encoding, a lightweight multi-pooling self-attention to model multi-scale global contextual relationships with good computational efficiency, and a convolutional feed-forward network for feature transformation and further location information learning. Finally, a simple but effective decoder module is proposed to gradually recover spatial details from the skip connections in the encoder. Extensive experiments on three datasets demonstrate the superiority and efficiency of our method compared with other CNN- and transformer-based networks.

cs.CV↗

arXiv2026

The Geometry of Semantic Space: A Continuous Geometric Framework for the Transformer Architecture

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle $\calE = \calM \times \R^d$. Beginning from a single geometric axiom -- that the token sequence forms a discrete $1$-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning $124$M to $8$B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the $ε^{-1/2}$ Lipschitz scaling calibration at machine precision ($R^2 = 1.000$), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the $\calO(1/\sqrt{k})$ thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

cond-mat.dis-nn↗

arXiv2025

Peri-LN: Revisiting Normalization Layer in the Transformer Architecture

Selecting a layer normalization (LN) strategy that stabilizes training and speeds convergence in Transformers remains difficult, even for today's large language models (LLM). We present a comprehensive analytical foundation for understanding how different LN strategies influence training dynamics in large-scale Transformers. Until recently, Pre-LN and Post-LN have long dominated practices despite their limitations in large-scale training. However, several open-source models have recently begun silently adopting a third strategy without much explanation. This strategy places normalization layer peripherally around sublayers, a design we term Peri-LN. While Peri-LN has demonstrated promising performance, its precise mechanisms and benefits remain almost unexplored. Our in-depth analysis delineates the distinct behaviors of LN strategies, showing how each placement shapes activation variance and gradient propagation. To validate our theoretical insight, we conduct extensive experiments on Transformers up to $3.2$B parameters, showing that Peri-LN consistently achieves more balanced variance growth, steadier gradient flow, and convergence stability. Our results suggest that Peri-LN warrants broader consideration for large-scale Transformer architectures, providing renewed insights into the optimal placement of LN.

cs.LG↗

arXiv2025

Application of Graph Based Vision Transformers Architectures for Accurate Temperature Prediction in Fiber Specklegram Sensors

Fiber Specklegram Sensors (FSS) are highly effective for environmental monitoring, particularly for detecting temperature variations. However, the nonlinear nature of specklegram data presents significant challenges for accurate temperature prediction. This study investigates the use of transformer-based architectures, including Vision Transformers (ViTs), Swin Transformers, and emerging models such as Learnable Importance Non-Symmetric Attention Vision Transformers (LINA-ViT) and Multi-Adaptive Proximity Vision Graph Attention Transformers (MAP-ViGAT), to predict temperature from specklegram data over a range of 0 to 120 Celsius. The results show that ViTs achieved a Mean Absolute Error (MAE) of 1.15, outperforming traditional models such as CNNs. GAT-ViT and MAP-ViGAT variants also demonstrated competitive accuracy, highlighting the importance of adaptive attention mechanisms and graph-based structures in capturing complex modal interactions and phase shifts in specklegram data. Additionally, this study incorporates Explainable AI (XAI) techniques, including attention maps and saliency maps, to provide insights into the decision-making processes of the transformer models, improving interpretability and transparency. These findings establish transformer architectures as strong benchmarks for optical fiber-based temperature sensing and offer promising directions for industrial monitoring and structural health assessment applications.

eess.IV↗

arXiv2025

Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization

The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform distributions pose a number of challenging mathematical questions. We focus on a special case that admits a gradient flow formulation in the spaces of probability measures on the unit sphere under a special metric, which allows us to give at least partial answers in a rigorous way. The arising mathematical problems resemble those recently studied in aggregation equations, but with additional challenges emerging from restricting the dynamics to the sphere and the particular form of the interaction energy. We provide a rigorous framework for studying the gradient flow, which also suggests a possible metric geometry to study the general case (i.e. one that is not described by a gradient flow). We further analyze the stationary points of the induced self-attention dynamics. The latter are related to stationary points of the interaction energy in the Wasserstein geometry, and we further discuss energy minimizers and maximizers in different parameter settings.

math.AP↗

arXiv2025

A Survey of Quantum Transformers: Architectures, Challenges and Outlooks

Quantum Transformers integrate the representational power of classical Transformers with the computational advantages of quantum computing. Since 2022, research in this area has rapidly expanded, giving rise to diverse technical paradigms and early applications. To address the growing need for consolidation, this paper presents the first comprehensive, systematic, and in-depth survey of quantum Transformer models. First, we delineate the research scope, focusing on improving Transformer parts with quantum methods, and introduce foundational concepts in classical Transformers and quantum machine learning. Then we organize existing studies into two main paradigms: PQC-based and QLA-based, with PQC-based paradigm further divided into QKV-only Quantum Mapping, Quantum Pairwise Attention, Quantum Holistic Attention. and Quantum-Assisted Optimization, analyzing their core mechanisms and architectural traits. We also summarize empirical results that demonstrate preliminary quantum advantages, especially on small-scale tasks or resource-constrained settings. Following this, we examine key technical challenges, such as complexity-resource trade-offs, scalability and generalization limitations, and trainability issues including barren plateaus, and provide potential solutions, including quantumizing classical transformer variants with lower complexity, hybrid designs, and improved optimization strategies. Finally, we propose several promising future directions, e.g., scaling quantum modules into large architectures, applying quantum Transformers to domains with inherently quantum data (e.g., physics, chemistry), and developing theory-driven designs grounded in quantum information science. This survey will help researchers and practitioners quickly grasp the overall landscape of current quantum Transformer research and promote future developments in this emerging field.

quant-ph↗

arXiv2025

Scattering Transformer: A Training-Free Transformer Architecture for Heart Murmur Detection

In an attempt to address the need for skilled clinicians in heart sound interpretation, recent research efforts on automating cardiac auscultation have explored deep learning approaches. The majority of these approaches have been based on supervised learning that is always challenged in occasions where training data is limited. More recently, there has been a growing interest in potentials of pre-trained self-supervised audio foundation models for biomedical end tasks. Despite exhibiting promising results, these foundational models are typically computationally intensive. Within the context of automatic cardiac auscultation, this study explores a lightweight alternative to these general-purpose audio foundation models by introducing the Scattering Transformer, a novel, training-free transformer architecture for heart murmur detection. The proposed method leverages standard wavelet scattering networks by introducing contextual dependencies in a transformer-like architecture without any backpropagation. We evaluate our approach on the public CirCor DigiScope dataset, directly comparing it against leading general-purpose foundational models. The Scattering Transformer achieves a Weighted Accuracy(WAR) of 0.786 and an Unweighted Average Recall(UAR) of 0.697, demonstrating performance highly competitive with contemporary state of the art methods. This study establishes the Scattering Transformer as a viable and promising alternative in resource-constrained setups.

cs.SD↗

arXiv2026

Transformer Architectures as Complete Bayes Processes: A Formal Proof in the Measure-Theoretic Kernel Framework

We present a complete formal proof that transformer architectures, when their internal update mechanisms satisfy a Bayes joint-distribution condition, implement exact Bayesian posterior inference. Working within the measure-theoretic kernel framework, we define a hierarchy of abstractions -- from the core Bayesian transformer, through semantic transformers with explicit update kernels, to full transformer blocks with QKV/attention/residual/MLP pipelines, and finally multilayer stacks -- and prove at each level that the Bayes joint semantics implies the update kernel equals the posterior almost everywhere. For the block-level architecture, we derive the explicit Bayes formula through Radon-Nikodym differentiation and prove its normalization. We additionally prove that the softmax attention mechanism induces a valid probability distribution over keys, establishing the bridge between the abstract kernel framework and concrete attention implementations. The framework makes no architectural assumptions beyond the Markov kernel structure and exposes explicit conditions under which a transformer block is provably Bayesian. In essence, when this joint distribution condition is satisfied, the forward computation of a Transformer is formally equivalent to a rigorous Bayesian posterior update.

cs.LG↗

arXiv2023

Deep learning based on Transformer architecture for power system short-term voltage stability assessment with class imbalance

Most existing data-driven power system short-term voltage stability assessment (STVSA) approaches presume class-balanced input data. However, in practical applications, the occurrence of short-term voltage instability following a disturbance is minimal, leading to a significant class imbalance problem and a consequent decline in classifier performance. This work proposes a Transformer-based STVSA method to address this challenge. By utilizing the basic Transformer architecture, a stability assessment Transformer (StaaT) is developed {as a classification model to reflect the correlation between the operational states of the system and the resulting stability outcomes}. To combat the negative impact of imbalanced datasets, this work employs a conditional Wasserstein generative adversarial network with gradient penalty (CWGAN-GP) for synthetic data generation, aiding in the creation of a balanced, representative training set for the classifier. Semi-supervised clustering learning is implemented to enhance clustering quality, addressing the lack of a unified quantitative criterion for short-term voltage stability. {Numerical tests on the IEEE 39-bus test system extensively demonstrate that the proposed method exhibits robust performance under class imbalances up to 100:1 and noisy environments, and maintains consistent effectiveness even with an increased penetration of renewable energy}. Comparative results reveal that the CWGAN-GP generates more balanced datasets than traditional oversampling methods and that the StaaT outperforms other deep learning algorithms. This study presents a compelling solution for real-world STVSA applications that often face class imbalance and data noise challenges.

eess.SY↗

arXiv2025

CardioPatternFormer: Pattern-Guided Attention for Interpretable ECG Classification with Transformer Architecture

Accurate ECG interpretation is vital, yet complex cardiac data and "black-box" AI models limit clinical utility. Inspired by Transformer architectures' success in NLP for understanding sequential data, we frame ECG as the heart's unique "language" of temporal patterns. We present CardioPatternFormer, a novel Transformer-based model for interpretable ECG classification. It employs a sophisticated attention mechanism to precisely identify and classify diverse cardiac patterns, excelling at discerning subtle anomalies and distinguishing multiple co-occurring conditions. This pattern-guided attention provides clear insights by highlighting influential signal regions, effectively allowing the "heart to talk" through transparent interpretations. CardioPatternFormer demonstrates robust performance on challenging ECGs, including complex multi-pathology cases. Its interpretability via attention maps enables clinicians to understand the model's rationale, fostering trust and aiding informed diagnostic decisions. This work offers a powerful, transparent solution for advanced ECG analysis, paving the way for more reliable and clinically actionable AI in cardiology.

eess.SP↗